Simpsons's Rule Integration

Simpson's Rule uses parabolas to approximate the curve, represented in the above diagram by parabolas
f₁--f₂--f₃ and f₃--f₄--f₅. Simpson's Rule can be expressed as:

(f₁/3 + 4f₂/3 + 2f₃/3 + 4f₄/3 + ... + 2f_N-2/3 + 4f_N-1/3 + f_N/3)*dx

Simpson's Rule requires an even number of intervals (steps).

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